THERMAL EXPANSION PRACTICE PROBLEMS
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1 THERMAL EXPANSION PRACTICE PROBLEMS Thermal Expansion: A copper sphere has a diameter of cm and is at room temperature (20 C). An aluminum plate has a circular cut-out with a diameter of cm (also at room temperature). At what (common) temperature would the copper sphere just barely be able to pass through the hole in the aluminum plate? Thermal Expansion: A steel rod of circular cross-section and a diameter of 5.0 cm spans the 2.5-meter gap between two concrete fixtures. At 20 C the beam is not compressed and just touches each of the fixtures (exerting no force on them). What force is exerted on the fixtures when the temperature of the steel beam rises to 80 C, and the distance between the fixtures remains the same during the warming? The coefficient of expansion of steel is 1.1x10-5 C -1, and the Young's modulus of steel is 2.0x10-6 Pa. Ideal Gas Law: How many moles of carbon dioxide would there be in a 3.5- cm 3 CO 2 cartridge at room temperature (20 C) if the gauge pressure of the gas in the cartridge is 500 psi? How many molecules of carbon dioxide would there be in the cartridge?
2 IDEAL GAS LAW PRACTICE PROBLEMS Ideal Gas Law: An aerosol can contains a gas whose gauge pressure is 2.0 atm at 22 C. Suppose that the can will rupture when the gauge pressure of the gas inside rises to 3.5 atm. If the can were tossed into a fire, at what temperature will the can rupture? Ideal Gas Law: 66.0 ft 3 of air at atmospheric pressure and at 22 C is to be placed into a 10.0-liter scuba tank. Just after this transfer, it is found that the tank's gauge shows a pressure of 3000 psig. What temperature is the air immediately after the tank is filled? Ideal Gas Law: A bubble is released from the bottom of a fresh-water lake, 15.0 meters below the surface. The gas in the bubble is 4 C when released and warms to 20 C by the time it reaches the surface. If the bubble had a volume of 2.0 cm 3 at release, what will be its volume when it reaches the surface?
3 HEAT ENERGY PRACTICE PROBLEMS Heat Energy: At Vernal Falls in Yosemite National Park, California, water in the Merced River plummets 97 meters from the rim of the falls to a pool below. What is the temperature increase of the water after dropping this distance? Hint: You need to consider two energy conversions. Heat Energy: Compute the amount of heat energy required to convert 10 grams of ice originally at -20 C to steam at 150 C? Heat Energy: A girl with a mass of 60 kg skis across a horizontal surface of ice. She finds that she is uniformly decelerating due to friction. If the kinetic coefficient of friction between the skis and ice is 0.30, and she travels 40 meters before coming to rest, how much ice melts during this process? Assume the ice initially is at 0 C.
4 CALORIMETRY PRACTICE PROBLEMS Calorimetry: A styrofoam cup contains 100 grams of water at 50 C. A 40-gram piece of ice at -20 C is placed in the cup, and the system is allowed to come to thermal equilibrium. Assuming the cup does not take part in any heat sharing, describe thermal equilibrium reached by the system. Calorimetry: A styrofoam cup contains 100 grams of water at 60 C. A 200- gram piece of ice at -40 C is placed in the cup, and the system is allowed to come to thermal equilibrium. Assuming the cup does not take part in any heat sharing, describe thermal equilibrium reached by the system. Calorimetry: A styrofoam cup contains 100 grams of water at 20 C. A 200- gram piece of ice at -60 C is placed in the cup, and the system is allowed to come to thermal equilibrium. Assuming the cup does not take part in any heat sharing, describe thermal equilibrium reached by the system.
5 HEAT TRANSPORT PRACTICE PROBLEMS Thermal Conductivity: A pane of glass is 1/8" thick and has dimensions 1.5 m by 2.5 m. It separates two heat reservoirs whose temperatures are 10 C and 22 C. What is the rate of heat transport through the pane? Thermal Conductivity: A copper and an aluminum cylinder are joined end-toend as shown. Each has a diameter of 4.0 cm and a length of 25.0 cm. One end of the copper cylinder is maintained at 90 C and one end of the aluminum cylinder is maintained at 15 C. What is the junction temperature? Thermal Radiation: The surface of a cube with sides of length 0.05 m has an emissivity of If the surface of the cube is maintained at a temperature of 550 C, what is the radiant energy flux through the surface of the cube?
6 ENTROPY PRACTICE PROBLEMS Warming: Find the change in entropy of a 250-gram piece of copper heated from 20 o C to 180 o C. Take the specific heat of copper to be.092 cal/g.o C. Phase Change: Find the change in entropy of a 1.5-kg mass of water (initially at 0 o C) when it is fully frozen, producing ice at 0 o C. Take the latent heat of fusion for H 2 O to be 2.26x10 6 J/K. Free Expansion: Find the change in entropy when an ideal gas at 1.0 atm and 20 o C occupying a chamber whose volume is 0.5 m 3 is allowed to free-expand into an evacuated chamber whose (extra) volume is 2.5 m 3. Compound: A 60-gram piece of ice at 0 o C is placed in a container with 200 grams of water at 50 o C. Find the temperature of this system after thermal equilibrium is attained. Use this result to find ΔS for: (1) the water; (2) the ice; and (3) the entire system during this process. Assume that the container does not transfer any heat energy.
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